If , Question.7. z, and z, are four solutions for the equation ( 2i32 If z'Ζ,,23,24...
QUESTION 7. [7] Find all solutions to the equation cosh z = i. Express your answer(s) in rectangular (cartesian) form and make a neat sketch showing where the solutions lie in the complex plane. It is acceptable, but not necessary, to consider this exercise as finding and plotting all values of cosh-li.
Question 3 If (i) ,⅔and z, are four solutions for the equation (2-1) =-4 findz, (a) 1 23 , ,23and z4 1' "23
02. (2). If |2-3|=|z+il. (1). Use an algebraic method to find a Cartesian equation of the locus of 2 (11) Sketch the locus of zon an Argand diagram. (6). If are 9- (1). Sketch the locus of P(x,y) which is represented by z on an Argand diagram (i). Find the Cartesian equation of this locus. (c). Given that the complex number z=x+iy where x,y e Rssatisfies the equation 12-12-51 = 3, find the minimum value and the maximum value of...
and z2 = 1 1 + 3i 3-i a) Given that zı = find z such that z = 2 + i 4- ¿ 22 Give your answer in the form of a + bi. Hence, find the modulus and argument of z, such that -- < arg(2) < 7. (6 marks) b) Given w = = -32, i. express w in polar form. (1 marks) ii. find all the roots of 2b = -32 in the form of a...
Question 2. (a) Find all solutions : є C of the equation tan(z) = (1 + iVT)/4. (b) Verify that the solutions you claitm to have discovered do actually satisky the oqatio (c) Evaluate the following contour integral: dz tan(a) - 1-iv7 Question 2. (a) Find all solutions : є C of the equation tan(z) = (1 + iVT)/4. (b) Verify that the solutions you claitm to have discovered do actually satisky the oqatio (c) Evaluate the following contour integral:...
Show that the equation z 1 has one real root and two other roots which are not real, and that, if one of the non-real roots is denoted by w, the other s then . Mark on the Argand diagram the points which represent the three roots and show that they are the vertices of an equilateral triangle.
Find all solutions of the equation z² = 2
i Determine the three cube roots of 7-9j in complex polar form, using radialn (2 marks measure i Sketch the three cube roots from part i) on the Argand diagram. Use best practice for (2 marks the development of the graph. i Determine the three cube roots of 7-9j in complex polar form, using radialn (2 marks measure i Sketch the three cube roots from part i) on the Argand diagram. Use best practice for (2 marks the development of...
For the complex number given as: z = a + bi / c+di where i = √−1 is the imaginary unit. The parameters are defined as a = √2, b = 0, c = 0.5 and d = −0.5. (a) Find the real and the imaginary parts of z, and then draw the Argand dia- gram. (Hint: Use the conjugate of the denominator.) 2.5 (b) Based on the Argand diagram, find the distance r of the complex number z from...
Claim: there are no integer solutions to the equation 3x + 21y = 7. How might our proof by contradiction start? Select one: O a. Suppose not. That is, suppose there are non-integers x and y such that 32 +21y = 7. b. Suppose not. That is, suppose there are integers x and y such that 3x + 21y = 7. O c. Suppose not. That is suppose that there are integers x and y such that 32 +217 +...